The problem that came first
Before there was any use for a general source of power, there was a specific and expensive nuisance: coal mines fill with water.
Dig below the water table and groundwater seeps in continuously. Bail it out with horses turning a winding gear and the cost rises with depth, because the water must be lifted further and there is more of it. By the early eighteenth century British mines were reaching depths where the horse teams cost more than the coal was worth, and shafts were being abandoned while still productive.
Key idea: The first steam engines were not built to power anything. They were built to lift water out of holes, and they were installed at coal mines because that is where both the problem and the free fuel were. Everything the technology became followed from improvements to a machine designed for that single job.

